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All Journal InPrime: Indonesian Journal Of Pure And Applied Mathematics
Mohammad Ghani
School of Mathematics and Statistics, Northeast Normal University
Computer Science & IT Mathematics

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Numerical Results of Crank-Nicolson and Implicit Schemes to Laplace Equation with Uniform and Non-Uniform Grids Mohammad Ghani
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 3, No 2 (2021)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v3i2.20917

Abstract

AbstractIn this paper, we investigate the numerical results between Implicit and Crank-Nicolson method for Laplace equation. Based on the numerical results obtained, we get the conclusion that the absolute error of Crank-Nicolson method is smaller than the absolute error of Implicit method for uniform and non-uniform grids which both refer to the analytical solution of Laplace equation obtained by separable variable method.Keywords: Crank-Nicolson; Implicit; Laplace equation; separable variable method; uniform and non-uniform grids. AbstrakDalam makalah ini, kami menyelidiki hasil numerik antara etode Implisit dan Crank-Nicolson untuk persamaan Laplace. Berdasarkan hasil numerik yang diperoleh, kita mendapatkan kesimpulan bahwa kesalahan absolut metode Crank-Nicolson lebih kecil daripada kesalahan absolut metode Implisit untuk grid seragam dan tak-seragam yang keduanya mengacu pada solusi analitik persamaan Laplace yang diperoleh dengan metode separable.Kata kunci: Crank-Nicolson; Implisit; persamaan Laplace; metode variable terpisah; grid seragam dan tak-seragam.
Space-Time and Motion to Advection-Diffusion Equation Mohammad Ghani
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 3, No 1 (2021)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v3i1.19679

Abstract

AbstractWe are concerned with the study the differential equation problem of space-time and motion for the case of advection-diffusion equation. We derive the advection-diffusion equation from the conservation of mass, where this can be represented by the substance flow in and flow out through the medium. In this case, the concentration of substance and rate of flow of substance in a medium are smooth functions which is useful to generate advection-diffusion equation. A special case of the advection-diffusion equation and numerical results are also given in this paper. We use explicit and implicit finite differences method for numerical results implemented in MATLAB.Keywords: advection-diffusion; space-time; motion; finite difference method. AbstrakKami tertarik untuk mempelajari masalah persamaan diferensial ruang-waktu, dan gerak untuk kasus persamaan adveksi-difusi. Kita menurunkan persamaan adveksi-difusi dari kekekalan massa, di mana hal ini dapat diwakili oleh aliran zat yang masuk dan keluar melalui media. Dalam hal ini konsentrasi zat dan laju aliran zat dalam suatu medium merupakan fungsi halus yang berguna untuk menghasilkan persamaan adveksi-difusi. Sebuah kasus khusus persamaan adveksi-difusi dan hasil numerik juga diberikan dalam makalah ini. Kami menggunakan metode beda hingga explisit dan implisit untuk hasil numerik yang diimplementasikan dalam MATLAB.Kata kunci: adveksi-difusi; ruang-waktu; gerak; metode beda hingga.
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